(2n+6)(3n-8)=

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Solution for (2n+6)(3n-8)= equation: 


Simplifying
(2n + 6)(3n + -8) = 0

Reorder the terms:
(6 + 2n)(3n + -8) = 0

Reorder the terms:
(6 + 2n)(-8 + 3n) = 0

Multiply (6 + 2n) * (-8 + 3n)
(6(-8 + 3n) + 2n * (-8 + 3n)) = 0
((-8 * 6 + 3n * 6) + 2n * (-8 + 3n)) = 0
((-48 + 18n) + 2n * (-8 + 3n)) = 0
(-48 + 18n + (-8 * 2n + 3n * 2n)) = 0
(-48 + 18n + (-16n + 6n2)) = 0

Combine like terms: 18n + -16n = 2n
(-48 + 2n + 6n2) = 0

Solving
-48 + 2n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + n + 3n2) = 0

Factor a trinomial.
2((-3 + -1n)(8 + -3n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3

Subproblem 2
Set the factor '(8 + -3n)' equal to zero and attempt to solve:

Simplifying
8 + -3n = 0

Solving
8 + -3n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3n = 0 + -8
-3n = 0 + -8

Combine like terms: 0 + -8 = -8
-3n = -8

Divide each side by '-3'.
n = 2.666666667

Simplifying
n = 2.666666667
Solution
n = {-3, 2.666666667}

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